Question

If a person travels for a certain number of hours at a speed of $x$ km/ hours and for an equal number of hours at a speed of $y$ km/hours, then his average speed for the whole journey must be

• A. The arithmetic mean of $x$ and $y$
• B. The geometric mean of $x$ and $y$
• C. The harmonic mean of $x$ and $y$
• D. None of the above

Answer 1

The correct option is C The harmonic mean of $x$ and $y$

Distance travelled in first $thrs.=xt.$
In next $t$ hours he covered distance $=yt$.
$\therefore$ Total distance $=(x+y)t.$ Total time $=2t$
$\therefore Speed=\frac{x+y}{2}$ (arithmetic mean).